标题： 感染和疫苗接种后抗体动力学的概率建模：一种马尔可夫链方法 显示英文标题

标题： Probabilistic Modeling of Antibody Kinetics Post Infection and Vaccination: A Markov Chain Approach

摘要： 理解抗体水平的动态变化对于描述对免疫事件（无论是感染还是疫苗接种）的时间依赖性反应至关重要。这些事件的顺序和时间显著影响抗体水平的变化。尽管近年来对该主题有广泛兴趣，并进行了许多实验研究，但免疫事件序列对抗体水平的影响仍未被充分理解。此外，疾病或疫苗在人群中的流行情况是随时间变化的。这结合个人抗体动力学的复杂性，使得分析来自人群的样本免疫测量变得困难。作为解决方案，我们设计了一个严格的数学表征，即一种时间非齐次马尔可夫链模型，用于事件间的转换，并结合一个概率框架来描述多个免疫事件后的抗体动力学。我们证明，这是一个理想的免疫事件序列模型，称为个人轨迹。这种新颖的建模框架通过严格跟踪人口抗体反应的概率分布随时间的变化，超越了易感-感染-恢复（SIR）表征。为了说明我们的观点，我们将数学框架应用于具有多次记录的感染和疫苗接种事件的个体的纵向严重急性呼吸综合征冠状病毒2（SARS-CoV-2）数据。我们的工作是全面理解抗体动力学的重要一步，这可能有助于有效分析自然免疫或疫苗的保护力，预测个体层面的遗漏免疫事件，并为加强剂的时间建议提供依据。 显示英文摘要

摘要： Understanding the dynamics of antibody levels is crucial for characterizing the time-dependent response to immune events: either infections or vaccinations. The sequence and timing of these events significantly influence antibody level changes. Despite extensive interest in the topic in the recent years and many experimental studies, the effect of immune event sequences on antibody levels is not well understood. Moreover, disease or vaccination prevalence in the population are time-dependent. This, alongside the complexities of personal antibody kinetics, makes it difficult to analyze a sample immune measurement from a population. As a solution, we design a rigorous mathematical characterization in terms of a time-inhomogeneous Markov chain model for event-to-event transitions coupled with a probabilistic framework for the post-event antibody kinetics of multiple immune events. We demonstrate that this is an ideal model for immune event sequences, referred to as personal trajectories. This novel modeling framework surpasses the susceptible-infected-recovered (SIR) characterizations by rigorously tracking the probability distribution of population antibody response across time. To illustrate our ideas, we apply our mathematical framework to longitudinal severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) data from individuals with multiple documented infection and vaccination events. Our work is an important step towards a comprehensive understanding of antibody kinetics that could lead to an effective way to analyze the protective power of natural immunity or vaccination, predict missed immune events at an individual level, and inform booster timing recommendations.